A month ago, I met the art historian Jonathan Katz in Washington DC. Katz was showing me around an exhibition he's co-curated at the Smithsonian's National Portrait Gallery, entitled Hide/Seek: Difference and Desire in American Portraiture. It is, amazingly, America's first major museum exhibition to look at art history from a homosexual perspective. "I have spent 15 years trying to get an exhibition like this at a major American museum," Katz told me, daring to dream that what he calls "the blacklist on queer representation in the US museum world" may be coming to an end. "If we're a hit, then I think we'll start seeing a different political atmosphere in American museums."

One month on, his dream is in tatters. Last week, after a sustained attack by opponents, including Republican House Speaker John Boehner and the Catholic League, the Smithsonian withdrew from Hide/Seek a video by the artist David Wojnarowicz, Fire in My Belly, which includes a crucifix covered in ants, symbolising the suffering of people with Aids; Wojnarowicz died of the disease in 1992. Georgia congressman Jack Kingston, railing against the gallery's depictions of "male nudity" and "Ellen DeGeneres grabbing her breasts", is calling for a congressional review of the Smithsonian's funding. Katz, who was not consulted before the artwork was pulled, is livid: "When the Smithsonian starts bowing to its censors, it abrogates its charge as our national museum."

All this heat is quite out of proportion with the actual show, which takes a queer-themed but uncontroversial look (at least by UK standards) at 100 years of art and social history. Works include The Shower-Bath (1917) by George Bellows, a scene of barely concealed homoeroticism in a public sauna. Modernist artist Marsden Hartley's Painting No 47, Berlin, ostensibly abstract, is revealed as a tribute to Hartley's dead lover, the German soldier Karl von Freyburg. "There's a painting from the same series in the Metropolitan Museum in New York," says Katz. "And there's no mention on the wall label of the love affair." No such reticence at Hide/Seek. Nearby hangs a hilarious photograph by Henri Cartier-Bresson, of the artist Charles Henri Ford emerging from a Parisian pissoir, his groin positioned next to a long, curling tongue on a billboard advertisement for "Krema".

You'd have to bury your head deeply in the sand to avoid these artworks' gay content. "But that's exactly what American museums have done," says Katz. Hide/Seek is the first show, he claims, to address the sexuality of two of America's major modern artists: Jasper Johns and Robert Rauschenberg. Their eight-year relationship in the 1950s is no secret. But there's a conspiracy of denial around the subject – to the extent that, when Katz tried to ask Rauschenberg about the relationship, at a press conference at New York's Guggenheim Gallery in 1995, he was evicted from the premises.

Finally, the show was programmed by the National Portrait Gallery, which relaunched in 2006 with a mission to chronicle the advance of civil liberties in the US. According to Katz, its director Martin Sullivan promised him that "[although] we know we are going to get bricks thrown at us, this show is the right and necessary thing to do". (Privately funded, the show is the NPG's most expensive ever.) But not everyone was that supportive. Securing loans was difficult, says Katz, because neither museums nor collectors want their artworks associated with homosexuality – which would (it is assumed) detract from their dollar value.

Besides which, American galleries are mainly private, and run by rich art collectors. "And the presumption is that those collectors are conservative. And you don't want to piss those people off." So was Katz denied loans to Hide/Seek? "Plenty. The museum asked me not to say which ones. But you'll notice that there aren't any major Rauschenberg combines. And there's no work by Cy Twombly. That's not irrelevant to this story."

Katz had been optimistic about remounting Hide/Seek with those missing artworks. But first, he had to demonstrate that America was ready for this debut major-museum exhibition of queer art. Hence his distress at last week's attack, and the way the Smithsonian capitulated. "When," Katz asks, "will the decent majority of Americans stand against a fringe that sees censorship as a replacement for debate?" Hide/Seek sought to conquer what Katz calls "the last acceptable prejudice in American political life" – but the conservative right, rampant after last month's midterm elections, won't relinquish their prejudices without a fight. And so, "an exhibition explicitly intended to break a 21-year blacklist against the representation of same-sex desire," says a dispirited Katz, "now finds itself in the same boat."